Finite Group Databasebeta

← Group #256607

Character table — Group #256607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444224444448888888888888888444444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-111-1-11-1-1-1-1-11-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-11-1-1-11-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1111-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111-11-1-11111-1-1-1-1
χ9111111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-11-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-11-1-1-1-1-111-1-111
χ11111111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-11111-1-1-1-111
χ12111111111111-1-1-1-11111-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1
χ13111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-111-11-1-1-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-11111-1-1-111-1-111-1-1
χ15111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-1111111-1-1-1-111
χ172222222222-2-2222222-2-2-2-2-2-2-222-20000000000000000000022002200-200000-200000000000
χ182222222222-2-2222222-2-2-2-2-2-2-222-200000000000000000000-2-200-2-200200000200000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2000000000000000000002200-2-200-200000200000000000
χ202222222222-2-2-2-2-2-222-2-22222-2-2-2-200000000000000000000-2-2002200200000-200000000000
χ2122222222-2-2222222-2-22222-2-2-2-2-2-20000000000000000000000220022000-2000-20000000000
χ2222222222-2-2222222-2-22222-2-2-2-2-2-20000000000000000000000-2-200-2-2000200020000000000
χ2322222222-2-222-2-2-2-2-2-222-2-222-222-200000000000000000000002200-2-2000-200020000000000
χ2422222222-2-222-2-2-2-2-2-222-2-222-222-20000000000000000000000-2-200220002000-20000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2222-2-22000000000000000022-2-200000000000000002-200000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2222-2-220000000000000000-2-2220000000000000000-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000000000000000022-2-20000000000000000-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-2-22200000000000000002-200000000
χ29222-22-2-2-22-22-200002-22-20000-2002000000002222-2-2-2-22i−2i2i−2i0000000000002i−2i000000000000
χ30222-22-2-2-22-22-200002-22-20000-2002000000002222-2-2-2-2−2i2i−2i2i000000000000−2i2i000000000000
χ31222-22-2-2-22-22-200002-22-20000-200200000000-2-2-2-222222i−2i2i−2i000000000000−2i2i000000000000
χ32222-22-2-2-22-22-200002-22-20000-200200000000-2-2-2-22222−2i2i−2i2i0000000000002i−2i000000000000
χ33222-22-2-2-2-22-220000-22-220000-20022222-2-2-2-2000000002i−2i−2i2i0000000002i−2i000000000000000
χ34222-22-2-2-2-22-220000-22-220000-20022222-2-2-2-200000000−2i2i2i−2i000000000−2i2i000000000000000
χ35222-22-2-2-2-22-220000-22-220000-2002-2-2-2-22222000000002i−2i−2i2i000000000−2i2i000000000000000
χ36222-22-2-2-2-22-220000-22-220000-2002-2-2-2-2222200000000−2i2i2i−2i0000000002i−2i000000000000000
χ3722-2-2-22-22-22002i2i−2i−2i2-200000002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i200002i−2i002-2000000000000i2−i22−20000
χ3822-2-2-22-22-22002i2i−2i−2i2-200000002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000−2i2i00-22000000000000−i2i2−220000
χ3922-2-2-22-22-22002i2i−2i−2i2-200000002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i200002i−2i002-2000000000000−i2i2−220000
χ4022-2-2-22-22-22002i2i−2i−2i2-200000002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i20000−2i2i00-22000000000000i2−i22−20000
χ4122-2-2-22-22-2200−2i−2i2i2i2-20000000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i200002i−2i00-22000000000000i2−i2−220000
χ4222-2-2-22-22-2200−2i−2i2i2i2-20000000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000−2i2i002-2000000000000−i2i22−20000
χ4322-2-2-22-22-2200−2i−2i2i2i2-20000000−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i200002i−2i00-22000000000000−i2i22−20000
χ4422-2-2-22-22-2200−2i−2i2i2i2-20000000−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i20000−2i2i002-2000000000000i2−i2−220000
χ452-2-2-22-22200222-22-200-2-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002-2002-200000000000000i2−i2i2−i2
χ462-2-2-22-22200222-22-200-2-22-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000-2200-2200000000000000−i2i2−i2i2
χ472-2-2-22-22200222-22-200-2-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002-2002-200000000000000−i2i2−i2i2
χ482-2-2-22-22200222-22-200-2-22-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000-2200-2200000000000000i2−i2i2−i2
χ492-2-2-22-2220022-22-2200-2-2-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002-200-2200000000000000−i2i2i2−i2
χ502-2-2-22-2220022-22-2200-2-2-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000-22002-200000000000000i2−i2−i2i2
χ512-2-2-22-2220022-22-2200-2-2-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000002-200-2200000000000000i2−i2−i2i2
χ522-2-2-22-2220022-22-2200-2-2-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000-22002-200000000000000−i2i2i2−i2
χ53444-44-4-4-44-4-4400004-4-440000400-40000000000000000000000000000000000000000000000
χ54444-44-4-4-4-444-40000-444-40000400-40000000000000000000000000000000000000000000000
χ5544-44-4-44-444000000-4-400000000002222−22−22−22−22222200000000000000000000000000000000000000
χ5644-44-4-44-444000000-4-40000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5744-44-4-44-4-4-4000000440000000000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000
χ5844-44-4-44-4-4-400000044000000000000000000−2i2−2i22i22i22i22i2−2i2−2i2000000000000000000000000000000
χ5944-4-4-44-444-4004i4i−4i−4i-440000000−4i4i00000000000000000000000000000000000000000000000
χ6044-4-4-44-444-400−4i−4i4i4i-4400000004i−4i00000000000000000000000000000000000000000000000
χ614-444-4-4-4400004i−4i−4i4i0000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000
χ624-444-4-4-4400004i−4i−4i4i000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000
χ634-444-4-4-440000−4i4i4i−4i0000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000
χ644-444-4-4-440000−4i4i4i−4i000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000
χ654-44-4-444-4000000000000004i−4i00002i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000000000
χ664-44-4-444-4000000000000004i−4i0000−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000000000
χ674-44-4-444-400000000000000−4i4i00002i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000000000
χ684-44-4-444-400000000000000−4i4i0000−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000000000
χ694-4-4444-4-4004-4000000-4400000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ704-4-4444-4-4004-4000000-440000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ714-4-4444-4-400-440000004-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ724-4-4444-4-400-440000004-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ734-4-4-44-44400-4-44-44-40044-440000000000000000000000000000000000000000000000000000
χ744-4-4-44-44400-4-4-44-4400444-40000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).